Economic Controls for Smart Water Distribution Networks Undergoing Supply Failures

Water distribution networks are designed and managed to provide adequate water flow to all users. Unexpected events, such as prolonged dry spells or cyber-physical attacks, can affect this status quo . Under water scarcity conditions, users located in high-pressure zones have a competitive advantage at the expense of the other customers, which, if exercised freely, can reduce the overall social welfare of the network, i.e., the value its customer get by using it. These conditions of supply failure are a challenge for water utilities, which can either provide full supply, but only for a limited time, or let the system uncontrolled, resulting in a substantial loss of social welfare. Here, we tackle the problem by adopting a game theoretic approach and develop a uniform pricing mechanism aimed to ensure an equitable and fair supply to all customers. The mechanism takes as input the users' demand—an information nowadays available through smart metering—and provides a pricing scheme that induces customers located in high-pressure zones to limit their demand, thus protecting the remaining users. Results obtained for a typical single-branch water distribution network show that the pricing mechanism attains good performance guarantees relative to the optimum, yet unattainable, water allocation. Our results also show that the performance of our pricing mechanism is often comparable to the one obtained by imposing flow restrictions to all users—whose implementation would require massive infrastructural upgrades. The opportunities we identify for supplying customers in an equitable and fair manner can extend to more complex topologies.